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NDA 2018 Maths · Mathematics · Straight Lines · hard

The point (1,1) lies inside the circle x^2+y^2=4. 2. The parabola y^2=8x passes through the point (2,-4).

Single correct option

Consider the following statements:
1. The point (1,1)(1,1) lies inside the circle x2+y2=4x^2+y^2=4.
2. The parabola y2=8xy^2=8x passes through the point (2,−4)(2,-4).
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (C) Both 1 and 2

For statement 1, 12+12=2<41^2+1^2=2<4, so the point is inside. For statement 2, substitute (2,−4)(2,-4): y2=16y^2=16 and 8x=168x=16, so the point lies on the parabola; the sign of yy does not matter because yy appears squared. Both statements are correct.
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Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake